Question

how cricket become popular in West indies

Answer 1

Cricket was introduced in West Indies by the British, as West Indies was colonized by them over a long duration.  During this period, the leisurely Britishers had not much work, but to play cricket.  They enjoyed playing the game with many local people doing all the hard work and slavery.

Local rich blacks too, were proud to join the British in playing the game and learning the game. One of the influences of learning English and being in company of the English. Stay in England also turned their interests.

Further playing cricket was something like a fashion, above the level of local West Indians. So the rich played it.  Cricket became popular also because they were strong and powerful.  They could hit the ball hard.  When they won their first few matches against the visitors (England), this became a national sport and obsession.